2.0 pembelajaran geometri_nota ringkas kuliah 2

8/3/2019 2.0 PEMBELAJARAN GEOMETRI_Nota Ringkas Kuliah 2

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PIAGET & INHELDER

Kognitif n geometry:

2-4 th pro kontekstual : belum dpapat membezakan 2d, 3d

4-7 th pra operasi : mula dapat membezakan 2d, 3d

7-11 th konkrit : mula memahami unsur logik, nombor, berat dan susunan. Formula luas

dan isipadu boleh diterapkan

The authors' investigations have been concerned with the order and manner in which

children begin to imagine or visualize the various spatial entities and spatial characteristics

of objects.

They report that the child first recognizes various objects by sense of touch alone and is

followed by building up and using certain primitive relationships. Contrary to the

historical development of geometry which began with treatment of straight lines, angles,

distances, and plane figures.

Piaget and Inhelder find that the child begins by noting the topological as opposed to the

metric properties of objects. He begins by ignoring straight lines, angles, parallels, and the

regular forms thereby constituted and considers only qualities such as closure, proximity,

separation and continuity.

From such beginnings he is finally able to deal with metric properties such as conservation

of direction, distance and relative operation. The child is thus able to establish a spatial

"schema" or network of dimensions in which the spatial properties of objects can be

organized. The authors develop the theories advanced in previous works to indicate the

nature of the psychological mechanisms required to mediate spatial properties and

endeavor to show the interrelationships between logical and psychological systems laid

down.


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VAN HIELES

Level 1:

Recognition. The student identifies, names, compares and operates on geometric figures

(e.g., triangles, angles, or intersecting) according to their appearance

Level 2:

Analysis. The student analyzes figures in terms of their components and relationship

among components and discovers properties/rules of a class of shapes empirically (e.g. by

folding, measuring, using grid or diagram).

Level 3:

Ordering. The student logically interrelates previously discovered properties / rules by

giving or following informal arguments.

Level 4:

Deduction. The student proves theorems deductively and established interrelationships

among networks of theorems.

Level 5:

Rigor/accurate. The students establishes theorems in different postulation systems and

analyzes/compares these systems


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HOFFER

Hoffer invented a two dimensional matrix to represent geometrical thinking: the

first dimension consists offive geometrical skills (Visual, Descriptive, Drawing, Logical and

Applied). The second one deals with the levels of geometric thinking (Recognition,Observation, Analysis, Ordering, Deduction and Abstraction). (Hoffer, 1981, p15).

The three geometric skills (Visual, Descriptive and Logical) and three levels of

geometrical thinking (Recognition, Analysis and Deduction).

Table (1): the levels of geometric thinking distributed according to geometric skills.

Level

Skill

Recognition Analysis Deduction

Visual

Recognize geometric

shapes by its' picture

without knowing the

shapes prosperities

Recognize the

relationship between

different kinds of

geometric shapes

Uses information about

a geometric shape to

deduce more

information

Descriptive

Naming a geometric

shape. Explain

statements that describe

geometric shape

Describes the

relationships between

geometric shapes.

Defines geometric

concepts clearly.

Understand the

difference between the

definition, postulate

and theorem

Logical

Understand the meaning

of shape reservation in

different situations.

Uses the properties of

geometric shapes to

identify the subset

relation

Uses logic to prove and

being able to deduce

new knowledge from

given facts

2.0 pembelajaran geometri_nota ringkas kuliah 2

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